Thursday, 14 April 2016

calculus - Convergence test from Demidovich: suminftyn=1fracnn+frac1n(n+frac1n)n



I'm just learning how to test series for convergence and have encountered this series from the Demidovich's book and I can't really decide what criteria should I use. Could you please give me some hint(s)?



n=1nn+1n(n+1n)n


Answer



Hint: Since n1/n1, you can forget about it. We're left with an nth term equal to




nn(n+1/n)n=(11+1/n2)n.


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